Kepler took Copernicusí heliocentric view of the universe and removed the requirement that the planets move in circular orbits at constant speeds. But that was only after he exhausted every combination of circular motions he could conceive.
Basing his work on the meticulous and exceedingly accurate naked-eye observations of the Danish astronomer Tycho Brahe, Kepler tried for more than a decade to match the positions of Mars to some sort of circular motion. Only after he ran out of possibilities did he try to fit the observations with another type of curve called an ellipse, the next-simplest form after the circle. He found that the positions of Mars matched almost perfectly with an elliptical path, and that the other planets followed suit.
This became the first of his three laws of planetary motion. He next tackled the problem of the planetsí varying speeds. He determined that a planet travels most rapidly when it comes closest to the Sun and moves slowest when farthest away. His third and final law of planetary motion gives the precise relation between the distance of a planet from the Sun and how fast it completes an orbit.